Perceptual learning refers to the improvement in performance in perceptual tasks through learning or practice. Often, this learning is partially or wholly specific to stimulus features of the task, such as rotation of the stimulus or change of visual position. In this study, we investigated transfer (or conversely specificity) as a function of the extent of initial practice for tasks that differed in stimulus orientation and position. We chose to test a moderate-precision orientation discrimination task known to exhibit partial transfer (Jeter et al., VSS, 2004) so that the extent of transfer after different amounts of initial learning could be assessed. Subjects discriminated the orientation (clockwise or counter-clockwise of a base angle) of a peripheral Gabor in initial training (i.e., -35°±5° or 55°±5°) with locations such as the NW and SE positions and in a 90° rotated transfer task in the NE and SW positions. Discrimination was trained and tested in the presence and absence of white external noise. Staircase methods measured contrast thresholds as a function of practice. As expected, the results show improvements in initial performance for the transfer task following 4 blocks (2 days) and 8 blocks (4 days) of initial training compared to 0 (no) initial training. Initial training and training after transfer had approximately equal power function rates. Additional blocks of initial training yielded little improvement in the transfer task. These results were not consistent with a simple model in which each initial training block yielded a (fractional) benefit at transfer (p [[lt]] 0.001), but may suggest saturating benefits with additional practice. These results are considered in the context of previous examples of perceptual learning in the literature.